Does the infinite series Sigma n=1 (1 / n + 5) converge or diverge?

Does the infinite series ∞ Sigma n=1 (1 / n + 5) converge or diverge? If the series converges state the value that it converges to.

Please show every step of how to figure this out. Which test should I be using? I see that with Harmonic Series that 1/n diverges so should I be using this Harmonic Series test?

Also does the infinite sequence { 1 / (n +5) } ∞ n=1, converge or diverge? If the sequence converges state the value that it converges to? I tried using the Test for Divergence, and got the limit as 0. But I read that this Test for Divergence when you get a result of 0 as the limit doesn't prove that you have convergence. Is this true? If so, which test should I be using for this sequence to test for convergence or divergence?

Thanks so much.